Calculate Ro for CS MOSFET Amp using V'A, L, and ID | Homework Solution

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To calculate Ro for a CS MOSFET amplifier, the formula Ro = V'A * L / ID is used, where V'A is given as 10 V/μm, L as 0.4 μm, and ID as 100 μA. The initial calculation yields a result of 4 x 10^-8, which appears incorrect compared to the book's answer of 40 kΩ. The confusion arises from unit handling; V'A in V/μm must be treated correctly in the formula. The correct calculation shows that when units are properly canceled, the result is indeed 40,000 ohms. Understanding the unit conversions is crucial for accurate results in this context.
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Homework Statement


Supposed to find Ro for a CS MOSFET amp given V'A=10V/μm, L=0.4μm, and ID=100μA.

Homework Equations



Ro=ro=V'A*L/ID

The Attempt at a Solution



I say that ro=10μ*0.4μ/100μ=
10*10^-6*0.4*10^-6/100*10^-6
= 4*10^-8

Book says "10x0.4/.1=40kΩ"

.. what exactly went into that? for one thing (10*0.4)/.1 does not = 40,000.

also if you multiply something in micrometers by something in micrometers, then divide by something in microamps, you should end up with a very small number, I think.

I'm sure 40kΩ makes sense somehow but they're doing a bad job of explaining it.
 
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Nevermind, I got it. V'A was in units of V/um, so really 10*(V/um)

[(10*(V/um))(0.4*um)]/(100*uA)=(10*V*0.4)/(100*uA)=40,000 ohm

^ because the um cancels out in numerator, ^ becomes just 4 V
 

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